Molecular Simulations of Zeolites: Adsorption, Diffusion, and Shape Selectivity

Size-sieving separation of hard-sphere gases at low concentrations through cylindrically porous membranes

Membranes are compelling devices for many industrial separation processes, which are all subject to the intrinsic permeability-selectivity tradeoff. A general strategy to enhance separation performance is to reduce the pore size distribution and, ideally, make the membrane isoporous. In this study, we focus on a minimal model for regularly porous membranes, which consists of hard spheres moving through cylindrical pores. The collision dynamics is solved exactly and implemented in nonequilibrium event-driven molecular dynamics simulations. For such size-sieving porous membranes, we show that the permeability P of hard spheres of size σ through cylindrical pores of size d follows the hindered diffusion mechanism due to size exclusion as P ∝ (1 - σ/d)². According to this law, the separation of binary mixtures of large and small particles exhibits a linear relationship between α^-1/2 and P^-1/2, where α and P are the selectivity and permeability of the smaller particle, respectively. The mean permeability through polydisperse pores is the average of the permeabilities of individual pores, weighted by the fraction of the single pore area over the total pore area.

Catalytic Depolymerization of Waste Polyolefins by Induction Heating: Selective Alkane/Alkene Production

Low- and high-density polyethylene (LDPE/HDPE) have been selectively depolymerized, without added H2, to C2-C20 + alkanes/alkenes via energy-efficient radio frequency induction heating, coupled with dual-functional heterogeneous Fe3O4 and Ni- or Pt-based catalysts. Fe3O4 was used to locally generate heat when exposed to magnetic fields. Initial results indicate that zeolite-based Ni catalysts are more selective to light olefins, while Ni supported on ceria catalysts are more selective to C7-C14 alkanes/alkenes. LDPE conversions up to 94% were obtained with minimal aromatic, coke, or methane formation which are typically observed with thermal heating. Two depolymerization mechanisms, a reverse Cossee-Arlman mechanism or a random cleavage process, were proposed to account for the different selectivities. The depolymerization process was also tested on commercial LDPE (grocery bags), polystyrene, and virgin HDPE using the Ni on Fe3O4 catalyst, with the LDPE resulting in similar product conversion (∼48%) and selectivity as for virgin LDPE.

Nanoconfinement and mass transport in metal-organic frameworks

The ubiquity of metal-organic frameworks in recent scientific literature underscores their highly versatile nature. MOFs have been developed for use in a wide array of applications, including: sensors, catalysis, separations, drug delivery, and electrochemical processes. Often overlooked in the discussion of MOF-based materials is the mass transport of guest molecules within the pores and channels. Given the wide distribution of pore sizes, linker functionalization, and crystal sizes, molecular diffusion within MOFs can be highly dependent on the MOF-guest system. In this review, we discuss the major factors that govern the mass transport of molecules through MOFs at both the intracrystalline and intercrystalline scale; provide an overview of the experimental and computational methods used to measure guest diffusivity within MOFs; and highlight the relevance of mass transfer in the applications of MOFs in electrochemical systems, separations, and heterogeneous catalysis.

Chemically Accurate Vibrational Free Energies of Adsorption from Density Functional Theory Molecular Dynamics: Alkanes in Zeolites

We present a methodology to compute, at reduced computational cost, Gibbs free energies, enthalpies, and entropies of adsorption from molecular dynamics. We calculate vibrational partition functions from vibrational energies, which we obtain from the vibrational density of states by projection on the normal modes. The use of a set of well-chosen reference structures along the trajectories accounts for the anharmonicities of the modes. For the adsorption of methane, ethane, and propane in the H-CHA zeolite, we limit our treatment to a set of vibrational modes localized at the adsorption site (zeolitic OH group) and the alkane molecule interacting with it. Only two short trajectories (1–20 ps) are required to reach convergence (<1 kJ/mol) for the thermodynamic functions. The mean absolute deviations from the experimentally measured values are 2.6, 2.8, and 4.7 kJ/mol for the Gibbs free energy, the enthalpy, and the entropy term (−TΔS), respectively. In particular, the entropy terms show a major improvement compared to the harmonic approximation and almost reach the accuracy of the previous use of anharmonic frequencies obtained with curvilinear distortions of individual modes. The thermodynamic functions so obtained follow the trend of the experimental values for methane, ethane, and propane, and the Gibbs free energy of adsorption at experimental conditions is correctly predicted to change from positive for methane (5.9 kJ/mol) to negative for ethane (−4.8 kJ/mol) and propane (−7.1 kJ/mol).

Performance-Based Screening of Porous Materials for Carbon Capture

Computational screening methods have changed the way new materials and processes are discovered and designed. For adsorption-based gas separations and carbon capture, recent efforts have been directed toward the development of multiscale and performance-based screening workflows where we can go from the atomistic structure of an adsorbent to its equilibrium and transport properties at different scales, and eventually to its separation performance at the process level. The objective of this work is to review the current status of this new approach, discuss its potential and impact on the field of materials screening, and highlight the challenges that limit its application. We compile and introduce all the elements required for the development, implementation, and operation of multiscale workflows, hence providing a useful practical guide and a comprehensive source of reference to the scientific communities who work in this area. Our review includes information about available materials databases, state-of-the-art molecular simulation and process modeling tools, and a complete catalogue of data and parameters that are required at each stage of the multiscale screening. We thoroughly discuss the challenges associated with data availability, consistency of the models, and reproducibility of the data and, finally, propose new directions for the future of the field.

Effects of Pore Connectivity on the Sorption of Fluids in Nanoporous Material: Ethane and CO2 Sorption in Silicalite

Adsorption of fluids in nanoporous materials is important for several applications including gas storage and catalysis. The pore network in natural, as well as engineered, materials can exhibit different degrees of connectivity between pores. While this might have important implications for the sorption of fluids, the effects of pore connectivity are seldom addressed in the studies of fluid sorption. We have carried out Monte Carlo simulations of the sorption of ethane and CO2 in silicalite, a nanoporous material characterized by sub-nanometer pores of different geometries (straight and zigzag channel like pores), with varied degrees of pore connectivity. The variation in pore connectivity is achieved by selectively blocking some pores by loading them with methane molecules that are treated as a part of the rigid nanoporous matrix in the simulations. Normalized to the pore space available for adsorption, the magnitude of sorption increases with a decrease in pore connectivity. The increased adsorption in the systems where pore connections are removed by blocking them is because of additional, albeit weaker, adsorption sites provided by the blocker molecules. By selectively blocking all straight or zigzag channels, we find differences in the absorption behavior of guest molecules in these channels.

Sampling efficiency of the counting method for permeability calculations estimated with the inhomogeneous solubility-diffusion model

Permeability is a key property in various fields such as membrane technology for chemical separation and transport of substances through cell membranes. At the molecular scale, the counting method uses the number of membrane crossings in a conventional unbiased molecular dynamics simulation to predict the permeability. This contribution investigates under which conditions the counting method has insufficient statistics. An equation is derived for a compartmental model based on the inhomogeneous solubility-diffusion (Smoluchowski) model, giving insight into how the flux correlates with the solubility of permeants. This equation shows that a membrane crossing is a rare event not only when the membrane forms a large free energy barrier but also when the membrane forms a deep free energy well that traps permeants. Such a permeant trap has a high permeability; yet, the counting method suffers from poor statistics. To illustrate this, coarse-grained MD was run for 16 systems of dipalmitoylphosphatidylcholine bilayer membranes with different permeant types. The composition rule for permeability is shown to also hold for fluxes, and it is highlighted that the considered thickness of the membrane causes uncertainty in the permeability calculation of highly permeable membranes. In conclusion, a high permeability in itself is not an effective indicator of the sampling efficiency of the counting method, and caution should be taken for permeants whose solubility varies greatly over the simulation box. A practical consequence relevant in, e.g., drug design is that a drug with high membrane permeability might get trapped by membranes thus reducing its efficacy.

Thermal resistance effect on anomalous diffusion of molecules under confinement

Diffusion is generally faster at higher temperatures. Here, a counterintuitive behavior is observed in that the movement of long-chain molecules slows as the temperature increases under confinement. This report confirms that this anomalous diffusion is caused by the "thermal resistance effect," in which the diffusion resistance of linear-chain molecules is equivalent to that with branched-chain configurations at high temperature. It then restrains the molecular transportation in the nanoscale channels, as further confirmed by zero length column experiments. This work enriches our understanding of the anomalous diffusion family and provides fundamental insights into the mechanism inside confined systems.

Diffusion of confined fluids in microporous zeolites and clay materials

Fluids exhibit remarkable variation in their structural and dynamic properties when they are confined at the nanoscopic scale. Various factors, including geometric restriction, the size and shape of the guest molecules, the topology of the host, and guest-host interactions, are responsible for the alterations in these properties. Due to their porous structures, aluminosilicates provide a suitable host system for studying the diffusion of sorbates in confinement. Zeolites and clays are two classes of the aluminosilicate family, comprising very ordered porous or layered structures. Zeolitic materials are important due to their high catalytic activity and molecular sieving properties. Guest molecules adsorbed by zeolites display many interesting features including unidimensional diffusion, non-isotropic rotation, preferred orientation and levitation effects, depending on the guest and host characteristics. These are useful for the separation of hydrocarbons which commonly exist as mixtures in nature. Similarly, clay materials have found application in catalysis, desalination, enhanced oil recovery, and isolation barriers used in radioactive waste disposal. It has been shown that the bonding interactions, level of hydration, interlayer spacing, and number of charge-balancing cations are the important factors that determine the nature of diffusion of water molecules in clays. Here, we present a review of the current status of the diffusion mechanisms of various adsorbed species in different microporous zeolites and clays, as investigated using quasielastic neutron scattering and classical molecular dynamics simulation techniques. It is impossible to write an exhaustive review of the subject matter, as it has been explored over several decades and involves many research topics. However, an effort is made to cover the relevant issues specific to the dynamics of different molecules in microporous zeolites and clay materials and to highlight a variety of interesting features that are important for both practical applications and fundamental aspects.

Gating control effect facilitates excellent gas selectivity in a novel Na-SSZ-27 zeolite

A novel Na-SSZ-27 zeolite was demonstrated to possess excellent H2/CO2 diffusion selectivity of more than 100. This investigation highlights the crucial effect of the "gating control" of the 8-ring windows on the separation, where sodium cations act as gates to selectively control the diffusion of CO2 and promote the selectivity for H2.

Experimental and Theoretical Evidence for the Promotional Effect of Acid Sites on the Diffusion of Alkenes through Small-Pore Zeolites

The diffusion of saturated and unsaturated hydrocarbons is of fundamental importance for many zeolite‐catalyzed processes. Transport of small alkenes in the confined zeolite pores can become hindered, resulting in a significant impact on the ultimate product selectivity and separation. Herein, intracrystalline light olefin/paraffin diffusion through the 8‐ring windows of zeolite SAPO‐34 is characterized by a complementary set of first‐principle molecular dynamics simulations, PFG‐NMR experiments, and pulse‐response temporal analysis of products measurements, yielding information at different length and time scales. Our results clearly show a promotional effect of the presence of Brønsted acid sites on the diffusion rate of ethene and propene, whereas transport of alkanes is found to be insensitive to the presence of acid sites. The enhanced diffusivity of unsaturated hydrocarbons is ascribed to the formation of favorable π–H interactions with acid protons, as confirmed by IR spectroscopy measurements. The acid site distribution is proven to be an important design parameter for optimizing product distributions and separations.

Connecting theory and simulation with experiment for the study of diffusion in nanoporous solids

Nanoporous solids are ubiquitous in chemical, energy, and environmental processes, where controlled transport of molecules through the pores plays a crucial role. They are used as sorbents, chromatographic or membrane materials for separations, and as catalysts and catalyst supports. Defined as materials where confinement effects lead to substantial deviations from bulk diffusion, nanoporous materials include crystalline microporous zeotypes and metal–organic frameworks (MOFs), and a number of semi-crystalline and amorphous mesoporous solids, as well as hierarchically structured materials, containing both nanopores and wider meso- or macropores to facilitate transport over macroscopic distances. The ranges of pore sizes, shapes, and topologies spanned by these materials represent a considerable challenge for predicting molecular diffusivities, but fundamental understanding also provides an opportunity to guide the design of new nanoporous materials to increase the performance of transport limited processes. Remarkable progress in synthesis increasingly allows these designs to be put into practice. Molecular simulation techniques have been used in conjunction with experimental measurements to examine in detail the fundamental diffusion processes within nanoporous solids, to provide insight into the free energy landscape navigated by adsorbates, and to better understand nano-confinement effects. Pore network models, discrete particle models and synthesis-mimicking atomistic models allow to tackle diffusion in mesoporous and hierarchically structured porous materials, where multiscale approaches benefit from ever cheaper parallel computing and higher resolution imaging. Here, we discuss synergistic combinations of simulation and experiment to showcase theoretical progress and computational techniques that have been successful in predicting guest diffusion and providing insights. We also outline where new fundamental developments and experimental techniques are needed to enable more accurate predictions for complex systems.

Order and disorder in the adsorption model of repulsively interacting binary mixtures on triangular lattices: theory and Monte Carlo simulations

The problem of interacting binary mixtures adsorbed on triangular lattices has been studied by means of ground-state (GS) calculations, Monte Carlo (MC) simulations and exact counting of configurations on finite cells [the so-called cluster-exact approximation (CA)]. We focus on the case of repulsive intraspecies couplings and null interspecies interaction, where a rich variety of ordered phases is found in the adsorbed layer. Each surface structure is separated from a disordered state by a phase transition occurring at a finite temperature. The ordered phases are identified by means of GS analysis, and their dependence on temperature is studied by MC simulations and CA. Total and partial adsorption isotherms are obtained for values of the lateral interactions in the different regions of the phase diagram. MC results are compared with CA calculations. A very good coincidence is obtained between both methods, supporting the validity of the exact counting of states on finite cells as an adequate approach to describe the behavior of multicomponent competitive adsorption with adsorbate-adsorbate interactions.

Synergistically enhance confined diffusion by continuum intersecting channels in zeolites

In separation and catalysis applications, adsorption and diffusion are normally considered mutually exclusive. That is, rapid diffusion is generally accompanied by weak adsorption and vice versa. In this work, we analyze the anomalous loading-dependent mechanism of p-xylene diffusion in a newly developed zeolite called SCM-15. The obtained results demonstrate that the unique system of "continuum intersecting channels" (i.e., channels made of fused cavities) plays a key role in the diffusion process for the molecule-selective pathways. At low pressure, the presence of strong adsorption sites and intersections that provide space for molecule rotation facilitates the diffusion of p-xylene along the Z direction. Upon increasing the molecular uptake, the adsorbates move faster along the X direction because of the effect of continuum intersections in reducing the diffusion barriers and thus maintaining the large diffusion coefficient of the diffusing compound. This mechanism synergistically improves the diffusion in zeolites with continuum intersecting channels.

Competitive Adsorption of Xylenes at Chemical Equilibrium in Zeolites

The separation of xylenes is one of the most important processes in the petrochemical industry. In this article, the competitive adsorption from a fluid-phase mixture of xylenes in zeolites is studied. Adsorption from both vapor and liquid phases is considered. Computations of adsorption of pure xylenes and a mixture of xylenes at chemical equilibrium in several zeolite types at 250 °C are performed by Monte Carlo simulations. It is observed that shape and size selectivity entropic effects are predominant for small one-dimensional systems. Entropic effects due to the efficient arrangement of xylenes become relevant for large one-dimensional systems. For zeolites with two intersecting channels, the selectivity is determined by a competition between enthalpic and entropic effects. Such effects are related to the orientation of the methyl groups of the xylenes. m-Xylene is preferentially adsorbed if xylenes fit tightly in the intersection of the channels. If the intersection is much larger than the adsorbed molecules, p-xylene is preferentially adsorbed. This study provides insight into how the zeolite topology can influence the competitive adsorption and selectivity of xylenes at reaction conditions. Different selectivities are observed when a vapor phase is adsorbed compared to the adsorption from a liquid phase. These insight have a direct impact on the design criteria for future applications of zeolites in the industry. MRE-type and AFI-type zeolites exclusively adsorb p-xylene and o-xylene from the mixture of xylenes in the liquid phase, respectively. These zeolite types show potential to be used as high-performing molecular sieves for xylene separation and catalysis.

Bridging scales in disordered porous media by mapping molecular dynamics onto intermittent Brownian motion

Owing to their complex morphology and surface, disordered nanoporous media possess a rich diffusion landscape leading to specific transport phenomena. The unique diffusion mechanisms in such solids stem from restricted pore relocation and ill-defined surface boundaries. While diffusion fundamentals in simple geometries are well-established, fluids in complex materials challenge existing frameworks. Here, we invoke the intermittent surface/pore diffusion formalism to map molecular dynamics onto random walk in disordered media. Our hierarchical strategy allows bridging microscopic/mesoscopic dynamics with parameters obtained from simple laws. The residence and relocation times - t_A, t_B - are shown to derive from pore size d and temperature-rescaled surface interaction ε/k_BT. t_A obeys a transition state theory with a barrier ~ε/k_BT and a prefactor ~10^-12 s corrected for pore diameter d. t_B scales with d which is rationalized through a cutoff in the relocation first passage distribution. This approach provides a formalism to predict any fluid diffusion in complex media using parameters available to simple experiments.

Characterizing moisture uptake and plasticization effects of water on amorphous amylose starch models using molecular dynamics methods

Dynamics and thermophysical properties of amorphous starch were explored using molecular dynamics (MD) simulations. Using the OPLS3e force field, simulations of short amylose chains in water were performed to determine force field accuracy. Using well-tempered metadynamics, a free energy map of the two glycosidic angles of an amylose molecule was constructed and compared with other modern force fields. Good agreement of torsional sampling for both solvated and amorphous amylose starch models was observed. Using combined grand canonical Monte Carlo (GCMC)/MD simulations, a moisture sorption isotherm curve is predicted along with temperature dependence. Concentration-dependent activation energies for water transport agree quantitatively with previous experiments. Finally, the plasticization effect of moisture content on amorphous starch was investigated. Predicted glass transition temperature (T_g) depression as a function of moisture content is in line with experimental trends. Further, our calculations provide a value for the dry T_g for amorphous starch, a value which no experimental value is available.

Multiscale exploration of hydrocarbon adsorption and hopping through ZSM-5 channels - from Monte Carlo modelling to experiment

In this article the results of statistical MC modelling corroborated by the FT-IR spectroscopy and gravimetric adsorption studies of low aliphatic hydrocarbons in ZSM-5 (Si/Al = 28 or silicalite) are presented. The extension of the existing Dubbeldam's forcefield towards inclusion of the finite aluminium-containing zeolites is proposed and its applicability is verified experimentally for the sorption of linear and branched hydrocarbons. The FT-IR spectroscopy applicability to follow the kinetics of small hydrocarbon adsorption has been successfully verified by the application of the Crank solution for diffusion to spectroscopy derived results.

Too Many Materials and Too Many Applications: An Experimental Problem Waiting for a Computational Solution

Finding the best material for a specific application is the ultimate goal of materials discovery. However, there is also the reverse problem: when experimental groups discover a new material, they would like to know all the possible applications this material would be promising for. Computational modeling can aim to fulfill this expectation, thanks to the sustained growth of computing power and the collective engagement of the scientific community in developing more efficient and accurate workflows for predicting materials' performances. We discuss the impact that reproducibility and automation of the modeling protocols have on the field of gas adsorption in nanoporous crystals. We envision a platform that combines these tools and enables effective matching between promising materials and industrial applications.

Influence of Topology and Brønsted Acid Site Presence on Methanol Diffusion in Zeolites Beta and MFI

Detailed insight into molecular diffusion in zeolite frameworks is crucial for the analysis of the factors governing their catalytic performance in methanol-to-hydrocarbons (MTH) reactions. In this work, we present a molecular dynamics study of the diffusion of methanol in all-silica and acidic zeolite MFI and Beta frameworks over the range of temperatures 373–473 K. Owing to the difference in pore dimensions, methanol diffusion is more hindered in H-MFI, with diffusion coefficients that do not exceed 10 × 10−10 m2s−1. In comparison, H-Beta shows diffusivities that are one to two orders of magnitude larger. Consequently, the activation energy of translational diffusion can reach 16 kJ·mol−1 in H-MFI, depending on the molecular loading, against a value for H-Beta that remains between 6 and 8 kJ·mol−1. The analysis of the radial distribution functions and the residence time at the Brønsted acid sites shows a greater probability for methylation of the framework in the MFI structure compared to zeolite Beta, with the latter displaying a higher prevalence for methanol clustering. These results contribute to the understanding of the differences in catalytic performance of zeolites with varying micropore dimensions in MTH reactions.

Transferable Molecular Model of Woven Covalent Organic Framework Materials

Two woven covalent organic framework materials (COF-505 and COF-506) have been synthesized since 2016, and the latter demonstrated the ability to take up dyes and other small molecules. This opens the door to applications such as separations, sensing, and catalysis. However, accelerating the design of future woven materials by changing the chemistry of the "threads" will require a computational model for these materials. Since no such atomic-scale model exists, we have developed a protocol for optimizing a force field for woven materials which can be used as the input to molecular dynamics simulations. Their high density and elasticity made these COFs challenging to model at a semiempirical level. Our modeling approach required simultaneous optimization of lattice parameters and elasticity using density functional theory-derived energy barriers and available experimental results. We used this force field, parameterized to fit COF-505, without change, to predict the structure of COF-506. This model allowed us to predict an anisotropy in 505's elasticity and preferred directions for diffusion which cannot be seen experimentally. The pore size distribution for 506 is dominated by small pores (80% <10 Å dia.), though 5% of the pores are up to 20 Å in diameter. We confirmed the experimental result that gases (barring helium) do not diffuse appreciably in COF-505. We validated our (unaltered) force field model to accurately predict experimental uptake data for tetrahydrofuran and methyl orange dye in COF-506. We proposed an atomic-scale mechanism by which COF-505 becomes metallated and demetallated. In addition, in advance of experimental studies, we determined the ability of 505 to incorporate other metals, such as Zn and Fe, which might be considered artificial photosynthesis agents. These predictions validate that Cu was a particularly appropriate choice of metal center for the synthesis, showcasing the ability of this model to play a role in designing woven materials a priori.

ECNU-36: A Quasi-Pure Polymorph CH Beta Silicate Composed of Hierarchical Nanosheet Crystals for Effective VOCs Adsorption

A quasi-pure C_H polymorph of microporous zeolite beta, named ECNU-36, was obtained as a highly crystalline silicate using 1,5-bis(tetramethylimidazolium) hydroxide as organic structure-directing agent (OSDA) in fluoride media. An appropriate concentration of free fluoride in the synthetic mother liquor was crucial to purify the C_H -phase. The framework structure of ECNU-36 consists of polymorph C_H (>95 %) and polymorph B, elucidated by a combination of PXRD data, DIFFaX simulation, EDT, and HRTEM techniques. For the first time, the framework structure of beta C_H polymorph was directly confirmed and solved using electron diffraction data. The pure-silica ECNU-36 showed an unusual crystal morphology, composed of stacked nanosheets, with typical 17 nm thickness and exposed {100} facets, which exhibited attractive adsorption performance for hydrocarbons and aromatics.

Selective potassium uptake via biocompatible zeolite-polymer hybrid microbeads as promising binders for hyperkalemia

Patients with chronic kidney disease are at high risk of hyperkalemia that is associated with various life-threatening complications. Treatments primarily rely on orally administered potassium binding agents, along with low curative effects and various side effects. Herein, direct serum potassium uptake was realized via zeolite–heparin-mimicking-polymer hybrid microbeads. The preparation process involved the synthesis of the heparin-mimicking polymer via the in situ cross-linking polymerization of acrylic acid and N-vinylpyrrolidone in polyethersulfone solution, the fabrication of microbeads via zeolite-mixing, electro-spraying and phase-inversion, and the subsequent aqueous-phase modifications based on ion-exchange and metal-leaching. An ultra-high (about 88%) amount of zeolite could be incorporated and well locked inside the polymer matrix. Potassium uptake capability was verified in water, normal saline and human serum, showing high selectivity and fast adsorption. The microbeads exhibited satisfying blood compatibility, negligible hemolysis ratio, prolonged clotting time, inhibited contact activation, and enhanced antifouling property toward serum proteins and cells. The proposed approach toward zeolite–heparin-mimicking-polymer hybrid microbeads provided a cheap, efficient and safe treatment protocol of hyperkalemia for the high-risk patients.

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Zeolite–heparin-mimicking-polymer hybrid microbeads were prepared for potassium uptake.

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An ultra-high (~88%) amount of zeolite could be well locked inside the polymer matrix.

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Potassium uptake by microbeads exhibited high selectivity and fast adsorption.

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The microbeads exhibited excellent blood compatibility.

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The proposed method is cheap, efficient and safe to treat hyperkalemia.

Long-Time Non-Debye Kinetics of Molecular Desorption from Substrates with Frozen Disorder

The experiments on the kinetics of molecular desorption from structurally disordered adsorbents clearly demonstrate its non-Debye behavior at “long” times. In due time, when analyzing the desorption of hydrogen molecules from crystalline adsorbents, attempts were made to associate this behavior with the manifestation of second-order effects, when the rate of desorption is limited by the rate of surface diffusion of hydrogen atoms with their subsequent association into molecules. However, the estimates made in the present work show that the dominance of second-order effects should be expected in the region of times significantly exceeding those where the kinetics of H₂ desorption have long acquired a non-Debye character. To explain the observed regularities, an approach has been developed according to which frozen fluctuations in the activation energy of desorption play a crucial role in the non-Debye kinetics of the process. The obtained closed expression for the desorption rate has a transparent physical meaning and allows us to give a quantitative interpretation of a number of experiments on the desorption kinetics of molecules not only from crystalline (containing frozen defects) but also from amorphous adsorbents. The ways of further development of the proposed theory and its experimental verification are outlined.

Transfer Learning Study of Gas Adsorption in Metal-Organic Frameworks

Metal-organic frameworks (MOFs) are a class of materials promising for gas adsorption due to their highly tunable nanoporous structures and host-guest interactions. While machine learning (ML) has been leveraged to aid the design or screen of MOFs for different purposes, the needs of big data are not always met, limiting the applicability of ML models trained against small data sets. In this work, we introduce an inductive transfer learning technique to improve the accuracy and applicability of ML models trained with a small amount of MOF adsorption data. This technique leverages potentially shareable knowledge from a source task to improve the models on the target tasks. As demonstrations, a deep neural networks (DNNs) trained on H₂ adsorption data with 13 506 MOF structures at 100 bar and 243 K is used as the source task. When transferring knowledge from the source task to H₂ adsorption at 100 bar and 130 K (one target task), the average predictive accuracy on target tasks was improved from 0.960 (direct training) to 0.991 (transfer learning), and transfer learning works in 89.3% of the cases. We also tested transfer learning across different gas species (i.e., from H₂ to CH₄), with an average predictive accuracy of CH₄ adsorption being improved from 0.935 (direct training) to 0.980 (transfer learning), and transfer learning works in 82.0% of the cases. More importantly, transfer learning is shown to effectively improve the models on the target tasks with low accuracy from direct training. However, when transferring the knowledge from the source task to Xe/Kr adsorption, the transfer learning does not improve the predictive accuracy significantly and even makes it worse in ∼50.0% of the cases, which is attributed to the lack of common descriptors that is key to the underlying knowledge.

MOF-Based Membranes for Gas Separations

Metal-organic frameworks (MOFs) represent the largest known class of porous crystalline materials ever synthesized. Their narrow pore windows and nearly unlimited structural and chemical features have made these materials of significant interest for membrane-based gas separations. In this comprehensive review, we discuss opportunities and challenges related to the formation of pure MOF films and mixed-matrix membranes (MMMs). Common and emerging separation applications are identified, and membrane transport theory for MOFs is described and contextualized relative to the governing principles that describe transport in polymers. Additionally, cross-cutting research opportunities using advanced metrologies and computational techniques are reviewed. To quantify membrane performance, we introduce a simple membrane performance score that has been tabulated for all of the literature data compiled in this review. These data are reported on upper bound plots, revealing classes of MOF materials that consistently demonstrate promising separation performance. Recommendations are provided with the intent of identifying the most promising materials and directions for the field in terms of fundamental science and eventual deployment of MOF materials for commercial membrane-based gas separations.

Metal–Organic Framework (MOF) through the Lens of Molecular Dynamics Simulation: Current Status and Future Perspective

As hybrid porous structures with outstanding properties, metal–organic frameworks (MOFs) have entered into a large variety of industrial applications in recent years. As a result of their specific structure, that includes metal ions and organic linkers, MOFs have remarkable and tunable properties, such as a high specific surface area, excellent storage capacity, and surface modification possibility, making them appropriate for many industries like sensors, pharmacies, water treatment, energy storage, and ion transportation. Although the volume of experimental research on the properties and performance of MOFs has multiplied over a short period of time, exploring these structures from a theoretical perspective such as via molecular dynamics simulation (MD) requires a more in-depth focus. The ability to identify and demonstrate molecular interactions between MOFs and host materials in which they are incorporates is of prime importance in developing next generations of these hybrid structures. Therefore, in the present article, we have presented a brief overview of the different MOFs’ properties and applications from the most recent MD-based studies and have provided a perspective on the future developments of MOFs from the MD viewpoint.

A Fractal-Based Correlation for Time-Dependent Surface Diffusivity in Porous Adsorbents

Fluid–solid adsorption processes are mostly governed by the adsorbate transport in the solid phase and surface diffusion is often the limiting step of the overall process in microporous materials such as zeolites. This work starts from a concise review of concepts and models for surface transport and variable surface diffusivity. It emerges that the phenomenon of hindered surface diffusion for monolayer adsorption, which is common in zeolites, and models able to fit a non-monotonic trend of surface diffusivity against adsorbate solid phase concentration, have received limited attention. This work contributes to the literature of hindered diffusion by formulating a time-dependent equation for surface diffusivity based on fractal dynamics concepts. The proposed equation takes into account the contributions of both fractal-like diffusion (a time-decreasing term) and hopping diffusion (a time-increasing term). The equation is discussed and numerically analyzed to testify its ability to reproduce the possible different patterns of surface diffusivity vs. time.

Geometric landscapes for material discovery within energy-structure-function maps

Porous molecular crystals are an emerging class of porous materials formed by crystallisation of molecules with weak intermolecular interactions, which distinguishes them from extended nanoporous materials like metal-organic frameworks (MOFs). To aid discovery of porous molecular crystals for desired applications, energy-structure-function (ESF) maps were developed that combine a priori prediction of both the crystal structure and its functional properties. However, it is a challenge to represent the high-dimensional structural and functional landscapes of an ESF map and to identify energetically favourable and functionally interesting polymorphs among the 1000s to 10 000s of structures typically on a single ESF map. Here, we introduce geometric landscapes, a representation for ESF maps based on geometric similarity, quantified by persistent homology. We show that this representation allows the exploration of complex ESF maps, automatically pinpointing interesting crystalline phases available to the molecule. Furthermore, we show that geometric landscapes can serve as an accountable descriptor for porous materials to predict their performance for gas adsorption applications. A machine learning model trained using this geometric similarity could reach a remarkable accuracy in predicting the materials' performance for methane storage applications.

Separation Selectivity of CH4/CO2 Gas Mixtures in the ZIF-8 Membrane Explored by Dynamic Monte Carlo Simulations

Here we report a series of nonequilibrium dynamic Monte Carlo simulations combined with dual control volume (DCV-DMC) to explore the separation selectivity of CH₄/CO₂ gas mixtures in the ZIF-8 membrane with a thickness of up to about 20 nm. Meanwhile, an improved DCV-DMC approach coupled with the corresponding potential map (PM-DCV-DMC) is further developed to speed up the computational efficiency of conventional DCV-DMC simulations. Our simulation results provide the molecular-level density and selectivity profiles along the permeation direction of both CH₄ and CO₂ molecules in the ZIF-8 membrane, indicating that the parts near membrane surfaces at both ends play a key role in determining the separation selectivity. All densities initially show a sharp increase in the individual maximum within the first outermost unit cell at the feed side and follow a long fluctuating decrease process. Accordingly, the corresponding selectivity profiles initially display a long fluctuating increase in the individual maximum and follow a sharp decrease near the membrane surface at the permeation side. Furthermore, the effects of feed composition, temperature, and pressure on the relevant separation selectivity are also discussed in detail, where the temperature has a greater influence on the separation selectivity than the feed composition and pressure. More importantly, the predicted separation selectivities from our PM-DCV-DMC simulations are well consistent with previous experimental results.